How do I survive the first night outside?

At a basic level, nighttime is just a darker version of the day, but your passive NPCs (pigs, sheep, etc) stop spawning in most areas (since they only spawn where there is light) and aggressive ones (zombies, skeletons, spiders, etc) begin to spawn.

Dealing with each type of aggressive mob will take different strategies. You should read up on each type of mob at the Minecraft Wiki.

Generally-speaking, I'd suggest having a stone or iron sword (the 3rd and 2nd best weapons in the game according to damage they deal). A bow and arrows are also great since they allow you to fight at range, but arrows aren't as easy to make. If you go this route, remember that you can retrieve arrows after you fire them. This will cut down on how often you have to replenish your supply with new ones.

Armor will help, especially when you begin dealing with the more difficult mobs such as Creepers, which start hissing and explode when they get close. Taking some food for emergency healing is also a wise idea.

EDIT- In the current version of the game, food does not instantly heal you. Please keep this in mind while trying to survive.

You will be a-fightin' and a-runnin', so you should pack accordingly.

• Armor - You'll want a full set, and the stronger, the better. It's tough to get a full SE of diamond, but iron armor should serve you well.
• Weapons - A diamond sword or a couple iron ones. A bow and a couple stacks of arrows.
• Tools - A couple stacks of torches will be useful. You want enough so that you can plop them down all willy-nilly and not run out. You may also want a boat or two for aquatic getaways.
• Navigation equipment - It's easy to get turned around when fighting and running in the dark. A compass will help you find your way home (assuming you know where your spawn point is in relation to your home. A light-emitting tower might also be helpful.
• Food - Even with armor, you're going to take some damage. Take some pork chops. Have one or two in your action bar.

Survival strategy mostly consists of continuous running and always looking around you. Monsters will not spawn within a short distance around you, but if you stand still, they will continue to spawn outside that radius and it can get crowded.

Backing away while shooting or stabbing works well on most critters, and circle-strafing makes killing skeletons easy. Don't get backed into a corner, and don't run into a crowd of monsters. Throw down torches liberally so you can see. And if there are just too many of them, don't be afraid to run.

If you start to run out of life, you can always dig a "coffin" for yourself to wait the night out. The simple way is to dig down three blocks, then put a lid on your coffin. Wait in your dirt until you think it might be light out, then dig up your lid.

If you have some glass, you can have a transparent coffin lid so it's easy to figure out when it's day time.